This application claims the priority of German patent document 10 2008 011 388.3-55, filed Feb. 27, 2008, the disclosure of which is expressly incorporated by reference herein.
The present invention relates to a method and apparatus for operating a navigation satellite system, and in particular for parameterization of satellite orbits and/or for satellite clock corrections.
Determination of the position of a user terminal by means of pseudo ranges to navigation satellites, requires knowledge concerning the satellite orbits and the timing of corresponding satellite clocks (the two types of information being time-dependent). The GPS System (Global Positioning System), for example utilizes this type of knowledge. The conventional method of providing such information consists of the satellite-based dissemination of so-called osculating Keplerian orbital elements, including several additional corrections for representing the satellite orbits, as well as of polynomials of the second degree for the correction of the time inherent to the satellites.
These types of information, which are part of the so-called navigation message, represent only temporarily usable approximations. That is, their validity basically commences with their dissemination, and ends upon the reception of the next valid navigation message. Although a later use of the information is conceivable, the quality of the approximation diminishes with increasing use duration.
Correspondingly, this approach also applies to the GLONASS satellite navigation system, which is an alternative to the GPS, with the exception that, instead of the Keplerian elements, in this case, positions and velocities are sent which are used as initial values for the numerical integration of the satellite movement equations.
The provided satellite orbits and the satellite clock corrections are therefore piecewise-defined functions of time; there is no secondary condition during the transition from one time interval of the time line to the adjacent time intervals. This may be considered to be a generalization of the known piecewise polynomial splines.
The foregoing method of providing the necessary types of information for determining the position of the user terminal has several disadvantages, as follows:                There is a discontinuity during the transition from one navigation message to another, which may become noticeable as jumps of up to several meters in the determined satellite position and of several nanoseconds in the determined satellite clock time.        Updating of the necessary information requires the reception of all information of the pertaining segment of a navigation message. The use of earlier information is not provided.        In the least favorable case, determination of the position of the user terminal is not possible before a valid navigation message has been received completely. The pertaining time duration significantly determines the time to the first fix of the user terminal or acquisition time.        The precision of the navigation message cannot be increased without increasing its transmission frequency.        The navigation message is oriented especially toward the representation of Keplerian orbits: its flexibility for the purpose of describing trajectories of a different kind is very low.        
Some situations exist where these disadvantages complicate or even prevent the navigation by means of satellites; for example:                Monitoring potential movements of so-called reference stations by means of techniques which are differential with respect to time becomes difficult because of the discontinuity during the transition from one navigation message to another, since such discontinuities dominate the remaining differential behavior.        A so-called cold start may result in very high demands on the acquisition time for the most varied navigation applications. These include, for example, tracking whales by receivers mounted on the animal, underwater start of submarine-based rockets or cruise missiles, the departure of aircraft-based proximity weapons and vehicle navigation in city areas. What all of these applications have in common is navigation by means of satellites and the demand for a first fix which is as fast as possible but which, as a rule, must follow a cold start because a view of the satellites before the corresponding event is either impossible or at least difficult.        
It is therefore an object of the present invention to provide a method and apparatus for generating a sufficiently smooth and very flexible parameterization of satellite orbits and/or satellite clock corrections of a satellite.
Another object of the invention is to provide such a method and apparatus which permits an increase of the precision of the satellite position that can be calculated at the user terminal.
These and other objects and advantages are achieved by the method according to the invention, in which a first system of advancing differentiable functions (herein referred to as a first function system) with a high approximation quality and a long range of influence is provided to describe the satellite orbits and/or of the satellite clock corrections. As shown in FIG. 10, the satellite orbits and/or satellite clock corrections parameterized from the first function system are transmitted by a central ground processing unit 7 to one or more satellites 2 and then to a user device 6. Alternatively, the transmission may take place only by way of a ground infrastructure, without utilizing the space segment.
The system according to the invention for generating a sufficiently smooth and very flexible parameterization of satellite orbits and/or satellite clock corrections includes apparatus for implementing the method according to the invention.
As a result of the approach according to the invention, jumps in the disseminated satellite position and satellite velocity can be eliminated during changing of the messages sent by a navigations satellite, so that the position and velocity of the user terminal can be determined more easily and precisely. In addition, it becomes possible to use processing techniques that are differential with respect to the time.
Furthermore, the method according to the invention helps to shorten the necessary transmission time and transmission frequency of the navigation message from the ground station to the satellite, achieving an increase in the precision of the navigation message, without increasing the transmission time or transmission frequency. In addition, the method according to the invention achieves much greater flexibility when parameterizing satellite orbits and/or the satellite clock corrections. Thus, trajectories other than the conventional orbits can also be treated, such as those of non-stationary pseudolites (ground-based additional transmitters which can be used alone or in addition to navigation satellites.)
According to an embodiment of the invention, in addition, a second advancing system (referred to herein as a second function system) of at least continuous functions with a moderate approximation quality and a very short range of influence is used to parameterize the satellite orbits and/or to correct satellite clocks, such that a conversion to the first function system in particular by the user terminal is possible. It is thus advantageous that, for the second function system, all data in the satellite which are to be transmitted to the user system are obtained from the first function system. As a result, the transmission load from the central ground processing unit to the satellite are not increased by the second function system. By providing the second function system, the time within which the first navigation information is available (i.e., the time to first fix) can be significantly shortened.
In the method according to the invention, the functions of the first and/or second function systems are sufficiently smooth. That is depending on the applicable requirement, for example, they may be continuous, differentiable or continuously differentiable several times. They may even be continuously differentiable infinitely often.
It is also advantageous that there is one preset (finite) value respectively for both function systems, which value limits the number of the nonzero functions at an arbitrarily selected point in time. As a result, a user terminal requires no more than one fixedly preset amount of information at any point in time.
According to a further advantageous embodiment of the method of the invention, the approximation of the satellite orbits and/or of the satellite clock corrections takes place in an advancing manner. That is, when an approximation is started at a special time interval, the progression of this time interval by a preset time period means that several functions (of the function system) which were necessary for the start, are now no longer required. As a result, these functions will never again make a contribution at a considered point in time, while several new functions will contribute for the first time.
According to a further embodiment of the invention, the instructions for generating the first and the second function system permit control of the quality of the approximation and/or the above-mentioned number of functions. For a so-called rapid cold start (i.e., a short time to which the first fix is present), a simple and suitable conversion between the first and the second function system should be possible in both directions.
According to an embodiment of the invention, polynomial B-splines, non-uniform rational B-splines (so-called NURBS), generalized B-splines (such as the so-called Chebyshev B-splines) or so-called wavelets with a local support can be used as a first and/or second function system.
The approximation of the satellite orbits and/or of the satellite clock corrections are advantageously determined by means of a linear combination of the functions of the first function system. For this purpose, an approximating linear combination of a preset function is first determined at an arbitrary starting interval, only for that starting interval. This supplies the initial coefficients of the first function system. Furthermore, a subsequent interval (that is, following the starting interval) is determined such that the end points of the subsequent interval differ from the end points of the starting interval. The approximation of the preset function is then determined for the subsequent interval in that, except for the coefficients obtained so far, only information of the function for the subsequent interval has an influence. All additional coefficients for further subsequent intervals are inductively determined in an analogous manner.
In addition, in the method according to the invention, differing first and second function systems can be used to approximate the satellite orbits and the satellite clock corrections. Different first and/or second function systems can also be used to approximate the satellite orbits and the satellite clock corrections of different satellites.
According to a further embodiment, when the determined coefficients and additional necessary parameters are uniformly distributed over the time, the time necessary to determine the position of the satellite in the user terminal can be minimized, particularly by way of an independent transmission structure and/or by way of the second function system.
In the method according to the invention, the advancing function systems can be utilized directly within the computation process for restored precise orbits and clocks, and also for the precomputation of orbits and clock corrections. This has the advantage that orbit and clock messages can be generated which a priori are smooth to a certain degree. In addition, the coefficients can be used directly, and the orbit and clock correction data can thereby be provided without losses.
Other objects, advantages and novel features of the present invention will become apparent from the following detailed description of the invention when considered in conjunction with the accompanying drawings.